Panamanian rhymes with:
romanian, rumanian, tasmanian, albanian, arslanian, aslanian, bahrainian, hovnanian, jordanian, lithuanian, mediterranean, o'hanian, ohanian, pennsylvanian, pomeranian, romanian, rumanian, stepanian, subterranean, tanzanian, tasmanian, ukrainian, vartanian
Panamanian sounds like:
p.m., pabon, paean, pain, paine, paino, pam, pammy, pan, panam, panama, pane, panem, panini, pannone, pannu, panny, paone, papania, papin, papineau, papini, papon, pavon, pavone, pawn, pawnee, pay'n, payan, payin', payna, payne, peine, pen, pena, penh, penman, penn, penna, penney, pennie, penniman, pennino, penny, peon, peony, pepin, peppin, peyman, pham, phan, phen, phenom, phenomena, phenomenon, phinney, phippen, phnom, phone, phoneme, phoney, phony, piana, piano, pima, pimm, pin, pina, pine, pineau, pineo, pinho, pini, pinion, pinn, pinneo, pinney, pinnow, pino, piny, pinyan, pion, pippen, pippin, pm, pneumo, pneumonia, poem, pom, poma, pomona, pon, pony, poon, popham, poppen, ppm, puffin, puma, pun, puny, pymm, pyne